Method and System for Designing a Waveform for Data Communication

ABSTRACT

Embodiments herein disclose a method and system for designing a waveform for data communication. The method includes applying, by a phase rotation applying unit, a constellation specific phase rotation between consecutive data symbols in a data stream to obtain a constellation rotated data stream. Further, the method includes introducing, by a frequency domain pulse shaping filter, an inter symbol interference (ISI) between modulated data symbols of the constellation rotated data stream, such that the ISI develops the waveform of the constellated rotated data stream to be transmitted.

FIELD OF INVENTION

The present invention relates to wireless communication techniques, andmore particularly to a method and system for designing a waveform fordata communication. The present application is a National PhaseApplication for PCT application No. PCT/IB2015/055381 based on, andclaims priority to Indian Application Number 2196/CHE/2015 filed on 29Apr. 2015, the disclosure of which is hereby incorporated by reference.

BACKGROUND OF INVENTION

An Orthogonal Frequency Division Multiplexing (OFDM) technique hasemerged as a dominant modulation technique for wide area cellularapplications. However, the fifth generation (5G) wireless standards areexpected to support high data rate wide area cellular systems as well aslow data rate applications involving machine-to-machine communications(M2M), machine type communications (MTC)-popularly known as internet ofthings (IoT). The physical layer of 5G IoT has diverse requirements suchas support for large coverage area, high power amplifier efficiency forincreased battery life, support for ultra-low latencies at physicallayer level, support of massive number of low throughput devices andvery low out of band emissions (OBE). The Low OBE is mainly required forsituations where a system uses dynamic spectrum access principles or forcognitive radio techniques.

The OFDM has very high peak-to-average-power ratio (PAPR), high OBEcompared to single carrier systems. Filter bank multicarrier (FBMC) andgeneralized frequency division multiplexing (GFDM) has been proposed asan alternative to OFDM. Though Discrete

Fourier transform (DFT)-pre-coded-OFDM employing a square root raisedcosine (SQRC) frequency domain pulse shaping filter (FDPSF) with certainexcess bandwidth (BW) was proposed in to reduce the peak to averagepower ratio (PAPR), the fourth generation (4G) Long-Term-Evolution (LTE)uplink employed a rectangular FDPSF for bandwidth efficiency reasons.

Therefore, there is a need for proposing a DFT-pre-coded-OFDM anddevelop a waveform that offers significantly lower PAPR compared toexisting OFDM based techniques.

The above information is presented as background information only tohelp the reader to understand the present invention. Applicants havemade no determination and make no assertion as to whether any of theabove might be applicable as Prior Art with regard to the presentapplication.

SUMMARY

The principal object of the embodiments herein is to provide a methodand system for designing a waveform for data communication.

Another object of the invention is to provide a mechanism for applying aconstellation specific phase rotation between consecutive data symbolsin a data stream to obtain a constellation rotated data stream.

Another object of the invention is to provide a mechanism forintroducing an inter symbol interference (ISI) between modulated datasymbols of the constellation rotated data stream.

Another object of the invention is to provide a mechanism for applying awindow function on the data stream.

Accordingly the invention discloses a method for designing a waveformfor data communication. The method includes applying, by a phaserotation applying unit, a constellation specific phase rotation betweenconsecutive data symbols in a data stream to obtain a constellationrotated data stream. Further, the method includes introducing, by afrequency domain pulse shaping filter, an inter symbol interference(ISI) between modulated data symbols of the constellation rotated datastream, such that the ISI develops the waveform of the constellatedrotated data stream to be transmitted.

Accordingly the invention discloses a method for processing a receiveddata stream. The received data stream is in a form of waveform designedby a frequency domain pulse shaping filter. The method includesreceiving, by a receiving unit, the data stream. The data streamcomprises an inter-symbol interference (ISI) between modulated datasymbols, of the data stream, introduced by the frequency domain pulseshaping filter. Further, the method includes suppressing, by avector/matrix-valued filter, the ISI between the modulated data symbolsin the data stream. Furthermore, the method includes converting, aconverting unit, the received data stream to time domain for detectionof a signal after suppressing the ISI.

Accordingly the invention provides a transmitter for designing awaveform for data communication. The transmitter includes a phaserotation applying unit configured to apply a constellation specificphase rotation between consecutive data symbols in a data stream toobtain a constellation rotated data stream. A frequency domain pulseshaping filter is configured to introduce an inter symbol interference(ISI) between modulated data symbols of the constellation rotated datastream, such that the ISI develops the waveform of the constellatedrotated data stream to be transmitted.

Accordingly the invention provides a receiver for processing a receiveddata stream. The received data stream is in a form of waveform designedby a frequency domain pulse shaping filter. The receiver includes areceiving unit configured to receive the data stream. The data streamcomprises an inter-symbol interference (ISI) between modulated datasymbols, of the data stream, introduced by the filter. Avector/matrix-valued filter is configured to suppress the ISI betweenthe modulated data symbols in the data stream. A converting unit isconfigured to convert the received data stream to time domain fordetection of a signal after suppressing the ISI.

These and other aspects of the embodiments herein will be betterappreciated and understood when considered in conjunction with thefollowing description and the accompanying drawings. It should beunderstood, however, that the following descriptions, while indicatingpreferred embodiments and numerous specific details thereof, are givenby way of illustration and not of limitation. Many changes andmodifications may be made within the scope of the embodiments hereinwithout departing from the spirit thereof, and the embodiments hereininclude all such modifications.

BRIEF DESCRIPTION OF FIGURES

This invention is illustrated in the accompanying drawings, throughoutwhich like reference letters indicate corresponding parts in the variousfigures. The embodiments herein will be better understood from thefollowing description with reference to the drawings, in which:

FIG. 1 is a block diagram of various units present in a transmitterconfigured for designing a waveform for data communication, according tothe embodiments as disclosed herein;

FIG. 2 is a flow diagram illustrating a method for designing a waveformfor data communication, according to the embodiments as disclosedherein;

FIG. 3a shows the sequence of steps followed in generating a BPSKmodulated G-DFT-pre-coded-OFDM signal with linearized Gaussian pulseshaping, according to the embodiments as disclosed herein;

FIG. 3b shows the steps involved for designing the waveform for QAMsystems with arbitrary pulse shaping filter, according to theembodiments as disclosed herein;

FIG. 4a shows the sequence of steps involved in the design of afrequency domain pulse shaping filter using linearized Gaussian pulse,according to the embodiments as disclosed herein;

FIG. 4b shows the sequence of steps involved in the design of afrequency domain pulse shaping filter for any time domain pulse,according to the embodiments as disclosed herein;

FIG. 5 is a block diagram of various units present in a receiver,according to the embodiments as disclosed herein;

FIG. 6 is a flow diagram illustrating a method for processing a receiveddata stream, according to the embodiments as disclosed herein;

FIG. 7 shows the sequence of steps involved during signal reception inthe GMMSE receiver design. according to the embodiments as disclosedherein;

FIG. 8 shows the sequence of steps involved during signal reception thesingle user MMSE receiver design, according to the embodiments asdisclosed herein; and

FIG. 9 shows the sequence of steps during signal reception in the singleuser WL MMSE receiver design, according to the embodiments as disclosedherein.

DETAILED DESCRIPTION OF INVENTION

The embodiments herein and the various features and advantageous detailsthereof are explained more fully with reference to the non-limitingembodiments that are illustrated in the accompanying drawings anddetailed in the following description. Descriptions of well-knowncomponents and processing techniques are omitted so as to notunnecessarily obscure the embodiments herein. Also, the variousembodiments described herein are not necessarily mutually exclusive, assome embodiments can be combined with one or more other embodiments toform new embodiments. The term “or” as used herein, refers to anon-exclusive or, unless otherwise indicated. The examples used hereinare intended merely to facilitate an understanding of ways in which theembodiments herein can be practiced and to further enable those skilledin the art to practice the embodiments herein. Accordingly, the examplesshould not be construed as limiting the scope of the embodiments herein.

The embodiments herein achieve a method and system for designing awaveform for data communication. The method includes applying, by aconstellation specific phase rotation applying unit, a constellationspecific phase rotation between consecutive data symbols in a datastream to obtain a constellation rotated data stream. Further, themethod includes introducing, by a frequency domain pulse shaping filter(FDPSF), an inter symbol interference (ISI) between modulated datasymbols of the constellation rotated data stream, such that the ISIdevelops the waveform of the constellated rotated data stream to betransmitted.

Unlike conventional systems, the proposed method can design thewaveforms with very low peak-to-average-power-ration (PAPR) and smallbit error rate (BER) penalty.

The embodiments herein achieve a method and receiver for processing areceived data stream. The received data stream is in a form of waveformdesigned by a frequency domain pulse shaping filter. The method includesreceiving, by a receiving unit, the data stream. The data streamcomprises an inter-symbol interference (ISI) between modulated datasymbols, of the data stream, introduced by the frequency domain pulseshaping filter. Further, the method includes suppressing, by avector/matrix-valued filter, the ISI between the modulated data symbolsin the data stream. Furthermore, the method includes converting, aconverting unit, the received data stream to time domain for detectionof a signal after suppressing the ISI.

The proposed method can mitigate the ISI and self-interference caused bythe FDPSF. The proposed method implements conventional and widely linearfrequency domain multi-user user equalization techniques to mitigate theISI and self-interference introduced by the FDPSF.

Unlike conventional systems, the proposed frequency domain multi-useruser equalizer performs both ISI and self-interference mitigationjointly with low-implementation complexity. The proposed GMMSE type ofreceiver exploits the redundancy in the frequency domain signalstructure introduced by the FDPSG and therefore leads to very efficientmulti-user frequency domain equalizer.

Referring now to the drawings and more particularly to FIGS. 1 through9, where similar reference characters denote corresponding featuresconsistently throughout the figure, there are shown preferredembodiments.

FIG. 1 is a block diagram of various units present in a transmitter 100configured for designing a waveform for data communication, according tothe embodiments as disclosed herein. The transmitter 100 includes aphase rotation applying unit 102, a frequency domain pulse shapingfilter 104, a computing unit 106, a repeating unit 108, a sampling unit110, a digital to analog converter 112, and a window applying unit 114.The phase rotation applying unit 102 is configured to apply aconstellation specific phase rotation between consecutive data symbolsin a data stream to obtain a constellation rotated data stream. Thefrequency domain pulse shaping filter 104 is configured to introduce aninter symbol interference (ISI) between modulated data symbols of theconstellation rotated data stream, such that the ISI develops thewaveform of the constellated rotated data stream to be transmitted. Thefrequency domain pulse shaping filter 104 is configured to shape aspectrum of a spread signal, when the sampling factor is one or morethan one.

The computing unit 106 is configured to compute the multi-point DiscreteFourier Transform (DFT) of the constellation rotated data stream. Aftercomputing the multi-point DFT of the constellation rotated data stream,the repeating unit 108 is configured to repeat the constellation rotateddata stream in a frequency domain to obtain a spread signal.

In an embodiment, the sampling unit 110 is configured to sample alinearized Gaussian pulse using an over-sampling factor. In anembodiment, the over-sampling factor is one. In another embodiment, theover-sampling factor is greater than one. After sampling the linearizedGaussian pulse, the computing unit 106 is configured to compute amulti-point two-sided DFT of the sampled linearized Gaussian pulse toobtain the frequency domain pulse shaping filter.

In an embodiment, the data stream is mapped to a localized subcarrierafter introducing the ISI between the data symbols of the data stream.In another embodiment, the data stream is mapped to a distributedsub-carrier.

The computing unit 106 is configured to add a cyclic prefix, a cyclicsuffix or combination of both to the data stream after performing aninverse discrete Fourier transform (IDFT) on the data stream. In anotherembodiment, the computing unit 106 is configured to add the cyclicprefix, the cyclic suffix or combination of both to the data streamafter performing an Inverse Fast Fourier Transform (IFFT) on the datastream. After adding the cyclic prefix, the cyclic suffix or combinationof both to the data stream, the digital to analog converter 112 isconfigured to convert the data stream from the digital signal to theanalog signal.

After adding the cyclic prefix or the cyclic suffix or combination ofcyclic prefix and the cyclic suffix to the data stream, the windowapplying unit 114 is configured to apply the window function on the datastream.

The proposed transmitter 100 utilizes a time domain signalrepresentation that is distinct from the DFT-precoded-OFDM. The proposedtransmitter 100 utilizes the DFT-precoded-OFDM techniques that allowcertain amount of self-interference among the users throughorthogonal/non-orthogonal subcarrier mapping. The proposed transmitter100 allows the users to have unequal bandwidth, while prior-art GFDMdoes not permit this scenario.

Unlike conventional system, the transmitter 100 can implement FDPStechniques that introduce a controlled amount of ISI between modulationdata symbols for reducing the PAPR. In the special case of binarymodulation, the transmitter 100 can apply constellation rotation of90-degrees between consecutive data symbols of the user followed by DFTprecoding, user specific frequency domain spreading, and frequencydomain subcarrier level pulse shaping filtering.

The following operation and function explains the design and functioningof transmitter 100 for designing the waveform in detail:

In an embodiment, the transmitter 100 can be configured to design thewaveform for a single user case. The transmitter sends a block of Mi.i.d

$\underset{a}{{real}/}{complex}$

valued modulation alphabets with zero-mean and variance σ². Let a_(t)(1)denote the modulation data. Here, the transmitter 100 can apply aconstellation specific phase rotation θ(1) to obtain:x_(t)(1)=e^(jθ(l))a_(t)(l). The DFT preceding of the data streamx_(t)(l) is accomplished using a M-point DFT as

$\begin{matrix}{{{x(k)} = {{\sum\limits_{l = 0}^{M - 1}{{x_{t}(l)}e^{\frac{{- j}\; 2\pi\;{lk}}{M}}\mspace{14mu} k}} = 0}},\ldots\mspace{14mu},{M - 1}} & (1)\end{matrix}$

where l, k denote the discrete time and subcarrier indices,respectively, and x(M+k)=x(k). Alternative to (l), a two sided DFT canbe taken as:

${x(k)} = {{\sum\limits_{l = \frac{- M}{2}}^{\frac{M}{2} - 1}{e^{j\;{\theta_{t}{(l)}}}{x_{i,t}(l)}e^{\frac{{- j}\; 2\pi\;{lk}}{M}}\mspace{31mu}\frac{- M}{2}}} \leq k \leq {\frac{M}{2} - 1}}$

Consider a L fold periodic extension of x(k) where

${\overset{˜}{x}(m)} = {{x\left( {\left( {\left( {m + \frac{LM}{2}} \right){mod}\ M} \right) + 1} \right)}.}$

Here, the elements of the vector {tilde over (x)}(m) take the range

${m = {- \frac{LM}{2}}},\ldots\mspace{14mu},{\frac{LM}{2} - 1}$

and ML=N, N being total number of used subcarriers. In time domain,

${{\overset{˜}{x}}_{t}(n)} = {x_{t}\left( \frac{n}{L} \right)}$

for n=pL where p=0,1, . . . , M−1 and {tilde over (x)}(n)=0 elsewhereand

${n = {- \frac{N}{2}}},\ldots\mspace{14mu},{\frac{N}{2} - {1.}}$

Here

${x_{t}(l)} = {{\overset{˜}{x}}_{t}\left( {{lL} - \frac{N}{2}} \right)}$

for l=0, . . . , M−1. Let

$\begin{matrix}{{{{\overset{˜}{x}(m)} = {{\sum\limits_{n = \frac{- N}{2}}^{\frac{N}{2}}{{{\overset{˜}{x}}_{t}(m)}e^{\frac{{- 2}\;\pi\;{nn}}{N}}\mspace{34mu} m}} = \frac{- N}{2}}},,,{\frac{N}{2} - 1}}\mspace{155mu}} & {(2)} \\{= {\sum\limits_{l = 0}^{M - 1}{{x_{t}(1)}e^{\frac{{- j}2{\pi{({{lL} - \frac{N}{2}})}}m}{N}}}}} & {(3)} \\{= {e^{j\;\pi\; m}{\sum\limits_{l = 0}^{M - 1}{{x_{t}(l)}e\frac{{- j}\; 2\;\pi\;{lLm}}{N}}}}} & {(4)}\end{matrix}$

The DFT operation in (1) can also be implemented as a two-sided DFT with1 in the range

${\left\lbrack {\frac{- M}{2},\ldots\mspace{14mu},{\frac{M}{2} - 1}} \right\rbrack\left\lbrack {{{\left( {- M} \right)/2}\mspace{14mu}\ldots\mspace{20mu}{M/2}} - 1} \right\rbrack}.$

Alternatively, swap the left and right halves of x(k) with zerofrequency component in the middle. Now consider a frequency domain pulseshaping filter:

$\begin{matrix}{{{q(m)} = {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2} - 1}{{q_{t}(n)}e\frac{{- j}2_{i}\pi\; n\; m}{N}}}},\mspace{14mu}{m = {- \frac{N}{2}}},\ldots\mspace{14mu},{\frac{N}{2} - 1}} & (5)\end{matrix}$

Where q_(t) (n) are the samples of the time domain pulse shaping filter.Please note that, q(m) may take zero values for certain subcarriers.Alternatively, all N subcarriers need not be modulated with data. Insome cases, some subcarriers at band edges may be nulled out. Applyingthe pulse shape to the transmitted data {tilde over (x)}(m), theproposed method has: x_(q)(m)=q(m){tilde over (x)}(m). The time domainbaseband signal s(t) is obtained using an inverse discrete time Fouriertransform (IDFT).

$\begin{matrix}{{{s(t)} = {\frac{1}{N}{\sum\limits_{m = {- \frac{N}{2}}}^{\frac{N}{2} - 1}{{q(m)}{\overset{\sim}{x}(m)}e^{{j2\pi}\; m\;\Delta\;{f{({t - T_{CP}})}}}}}}},{t \in \left\lbrack {0,{T + {bT}}} \right\rbrack}} & (6)\end{matrix}$

where T is the useful portion of OFDMA symbol, T_(CP) is the duration ofthe cyclic prefix (CP) and Δf=1/T is the subcarrier spacing. Note thatb=1 when the system uses CP only and b=2 when the system uses cyclicprefix as well as cyclic suffix. Using (4) and (5), the analog signalcan be rewritten as

$\begin{matrix}{{{{s(t)} = {\frac{1}{N}{\sum\limits_{m = {- \frac{N}{2}}}^{\frac{N}{2} - 1}{e^{j\;\pi\; m}{q(m)}{\overset{\sim}{x}(m)}e^{{j2\pi}\; m\;\Delta\;{f{({t - T_{CP}})}}}}}}},{t \in \left\lbrack {0,{T + {bT}}} \right\rbrack}}\mspace{40mu}} & {(7)} \\{= {\frac{1}{N}{\sum\limits_{l = 0}^{M - 1}{{x_{t}(l)}{\sum\limits_{m = \frac{= {LM}}{2}}^{\frac{LM}{2} - 1}{{q(m)}e^{j\; 2\;\pi\;{m{({{\frac{1}{T}{({t - T_{CP}})}} - \frac{lL}{N} + \frac{1}{2}})}}}}}}}}} & {(8)} \\{= {\frac{1}{N}{\sum\limits_{l = 0}^{M - 1}{e^{j\;{\theta{(l)}}}{a_{t}(l)}{q_{p}\left( {t - T_{CP} - \frac{lT}{M} + \frac{T}{2}} \right)}}}}} & {(9)}\end{matrix}$

where

${q_{p}(t)} = {\sum_{m = {- \frac{N}{2}}}^{\frac{N}{2} - 1}{{q(m)}e^{j2\pi m\frac{t}{T}}}}$

and t ∈ [0, T+bT] is the time domain pulse shaping function andx_(t)(l)=e^(jθ(l))a_(t)(l). Note that q_(p)(t)=q_(p)(t +rT), r being aninteger. The transmitter 100 sends successive data blocks serially whereeach data block is limited to duration of T+bT_(CP) seconds. Here, thetime domain signal has a form similar to conventional SC-FDMA with q(t)being the pulse shaping function.

In another embodiment, let us consider the multiple access scenarios. Inthis scenario, the number of users shares the available bandwidthsimultaneously. Therefore, the both non-orthogonal and orthogonal userallocations may be considered, where the users may employ distinct pulseshapes with different bandwidth requirements. Assuming there are a totalof u users, let us denote the data of the i^(th) user with x_(i)(k)where

$\begin{matrix}{{{x_{i}(k)} = {\sum\limits_{l = 0}^{M_{i} - 1}{e^{j\;{\theta_{t}{(l)}}}{x_{i,t}(l)}e^{\frac{{- j}\; 2\pi\;{lk}}{M_{i}}}}}},{k = 0},\ldots\mspace{14mu},{M_{i} - 1}} & (10)\end{matrix}$

where Mi is the data length of the i^(th) user, θ_(i)(l) being theconstellation rotation employed by the i^(th) user data x_(i,t). Notethat the DFT operation in (10) can be implemented using a two sided DFTas

${x_{i}(k)} = {{\sum\limits_{l = \frac{- M_{i}}{2}}^{\frac{M_{i}}{2} - 1}{e^{j\;{\theta_{t}{(l)}}}{x_{i,t}(l)}e^{\frac{{- j}\; 2\;\pi\;{lk}}{M_{i}}}\mspace{11mu}\frac{- M_{i}}{2}}} \leq k \leq {\frac{M_{i}}{2} - 1}}$

Let {tilde over (x)}_(i)(m) denote the L_(i) fold periodic extension ofx_(i)(k) where L_(i)M_(i)=N and let q_(i)(l) be the FDPSF associatedwith this user that is defined as

$\begin{matrix}{{{{q_{i}(m)} = {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2} - 1}{{q_{i,t}(n)}e^{\frac{{- j}\; 2\;\pi\;{mn}}{N}}}}},{{{for}\mspace{14mu} m} = {- \frac{{\overset{\_}{M}}_{i}}{2}}},\ldots\mspace{14mu},{\frac{{\overset{\_}{M}}_{i}}{2} - 1}}\mspace{40mu}} & {(11)} \\{= {0\mspace{31mu}{elsewhere}}} & {(12)}\end{matrix}$

where, q_(i,n)(t) are the corresponding time domain samples. Note thatthe FDPSF takes non-zero values over M _(i) subcarriers where M_(i)−M_(i) is the excess number of subcarriers employed for the i^(th)user. In this case, (M _(i)−M_(i))Δf is denoted as the excess bandwidthemployed by the i^(th) user. Further, the users are frequencymultiplexed over the given the band of interest as

$\begin{matrix}{{{s_{i}(t)} = {\frac{1}{N}{\sum\limits_{m = {- \frac{N}{2}}}^{\frac{N}{2} - 1}{{q_{i}\left( {m - m_{i}} \right)}{{\overset{\sim}{x}}_{j}(m)}e^{j\; 2\pi\;\Delta\;{f{({t\; - T_{CP}})}}}}}}},{t \in \left\lbrack {0,{T + {bT_{CP}}}} \right\rbrack}} & (13)\end{matrix}$

where m_(i) is the frequency shift of the i^(th) user. The proposedmethod provides a non-orthogonal multicarrier signal, if the values ofm_(i) are set to integer multiples of M _(i).

In an embodiment, the proposed method

${choosesm_{i}} = {{\left( {i - 1} \right)M_{i}} - \frac{N - {\overset{\_}{M}}_{i}}{2}}$

for i=1, 2, . . . , u_(i). In another embodiment, the values of m_(i)are chosen based on the subcarrier mapping procedure employed by thetransmitter 100.

The transmitted signal can be represented in an alternative form as

$\begin{matrix}{{{s_{i}(t)} = {\frac{1}{N}{\sum\limits_{l = 0}^{M_{i} - 1}{e^{j\;{\theta{(l)}}}{a_{i,t}(l)}{q_{i,p}\left( {t - T_{CP} - \frac{lT}{M_{i}} + \frac{T}{2}} \right)}}}}},{t \in \left\lbrack {0,{T + {bT_{CP}}}} \right\rbrack}} & (14)\end{matrix}$

Where

${q_{i,p}(t)} = {\sum_{m = \frac{\;_{- N}}{2}}^{\frac{N}{2} - 1}{{q_{i}\left( {m - m_{i}} \right)}e^{j\; 2\;\pi\; m\frac{t}{T}}}}$

is the time domain pulse shaping function employed by the i^(th) user.Here, q_(i,p)(t)=q_(i,p)(t+rT), where r is an integer.

let

$\begin{matrix}{{q_{i,p}(t)} = {{\sum\limits_{m = \frac{- N}{2}}^{\frac{N}{2} - 1}{{q_{i}\left( {m - m_{i}} \right)}e^{j2\pi m\frac{t}{T}}t}} \in \left\lbrack {0,{T + {bT_{CP}}}} \right\rbrack}} & (15)\end{matrix}$

Using (11) and substituting m−mi =m1 in (15) to express q_(i)(t) inalternative form as

$\begin{matrix}{{q_{i,p}(t)} = {e^{j\; 2\;\pi\; m_{i}\frac{t}{T}}{\sum\limits_{m = \frac{- {\overset{\_}{M}}_{i}}{2}}^{\frac{{\overset{\_}{M}}_{i}}{2} - 1}{{q_{i}(m)}e^{j2\pi m\frac{t}{T}}}}}} & {{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}(16)} \\{= {{{q_{0,i}(t)}e^{{- j}\; 2\;\pi\; m_{i}\frac{t}{T}}\mspace{14mu} t} \in \left\lbrack {0,{T + {bT}_{CP}}} \right\rbrack}} & {(17)}\end{matrix}$

and

${q_{0,i}(t)} = {\sum_{m_{1} = \frac{- {\overset{\_}{M}}_{i}}{2}}^{\frac{{\overset{\_}{M}}_{i}}{2} - 1}{{q_{i}\left( m_{1} \right)}e^{j2\pi m\frac{t}{T}}}}$

is the baseband pulse shaping function used by the i^(th) user. Now thetransmitted signal may be rewritten as:

$\begin{matrix}{{s_{i}(t)} = {\frac{1}{N}{\sum\limits_{l = 0}^{M_{i} - 1}{e^{j\;{\theta_{i}{(l)}}}{a_{i,t}(l)}{q_{0,i}\left( {t - T_{CP} - \frac{lT}{M_{i}} + \frac{T}{2}} \right)}e^{j\; 2\;\pi\; m_{i}\frac{({t - T_{CP} - \frac{lT}{M_{i}} + \frac{T}{2}})}{T}}}}}} & (18)\end{matrix}$

In an embodiment, the total number of subcarriers is N. However, onlyN_(u) subcarriers out of N may be used by the transmitter 100. Theremaining (N−N_(u)) subcarriers do not carry the data. Furthermore, anumber of users are frequency multiplexed over the N_(u) subcarriers.The transmitted signal is given by

${s_{i}(t)} = {{\frac{1}{Nu}{\sum\limits_{m}{{q_{i}\left( {m - m_{i}} \right)}{{\overset{˜}{x}}_{i}(m)}e^{{j2\pi\Delta}\;{f{({t - T_{cp}})}}}\mspace{31mu} t}}} \in \left\lbrack {0,{T + {bT_{cp}}}} \right\rbrack}$

Here the transmitted signal spans over a group of subcarriers whoserange is dictated by the subcarriers occupies by the signal of thei^(th) user. Furthermore, the value of m_(i) is a system design featurethat can be used to control the amount of non-orthogonality introducedby the transmitter 100. The value of m_(i) may be set to M_(i), M _(i)or any other value. For example, setting the value of m_(i) in the range[0 M_(i)] increases the spectrum efficiency of the system. Anotheralternative is to choose the value of m_(i) in the range. [M_(i) M_(i)]. In certain cases, one may set the value of m_(i) to be zero, ifmultiple users or signals of multiple antennas are allowed to transmiton the same time frequency resource.

Symbol Windowing: As the transmit signal is confined to a period of oneOFDM symbol duration, effectively it imposes a rectangular windowfunction that leads to high OBE. In order to reduce OBE, the proposedtechniques employ alternative time domain window functions that offersmooth transitions at the OFDM symbol boundaries. The proposed methodincludes a cyclic prefix as well as cyclic postfix each of durationT_(CP). The analog signal can be rewritten as

$\begin{matrix}{{{s_{i}(t)} = {\frac{1}{N}{\underset{m = {- \frac{N}{2}}}{\sum\limits^{\frac{N}{2} - 1}}{{w(t)}{q_{i}\left( {m - m_{i}} \right)}{{\overset{˜}{x}}_{i}(m)}e^{j\; 2\;{\pi\Delta}\;{f{({T - T_{cp}})}}}}}}},} & {{~~~~~~~~~~~~~~~~~~}(19)} \\{t \in \left\lbrack {0,{T + {bT_{CP}}}} \right\rbrack} & \; \\{{= {\frac{1}{N}{\sum\limits_{l = 0}^{M_{i} - 1}{e^{J^{\theta_{i}{(l)}}}{a_{i,t}(l)}{w(t)}{q_{i,p}\left( {t - T_{CP} - \frac{lT}{M_{i}} + \frac{T}{2}} \right)}}}}},} & {(20)} \\{t \in \left\lbrack {0,{T + {bT_{CP}}}} \right\rbrack} & \;\end{matrix}$

Where, w(t) is the proposed window function defined over the interval t

[0, T+bT_(CP)] (that is designed as the OFDM symbol block duration). Thewindow w(t) is chosen such that it takes a constant value for theduration of the OFDM symbol that excludes cyclic prefix and suffix. Thewindow takes a constant value during a portion of the cyclic prefixand/or suffix and it tapers to a zero value at the block boundaries.Standard time domain window functions such as SQRC, RC, Hamming,Hanning, Bartltt window can be used.In an embodiment, the following RC window is used, where W and β aredesign parameters:

$W,\ {{t} \leq \frac{1 - \beta}{2W}}$${{w(t)} = {\frac{W}{2}\left( {1 + {\cos\left( {\frac{\pi W}{\beta}\left( {{t} - \frac{\left( {1 - \beta} \right)}{2W}} \right)} \right)}} \right)}},{\frac{1 - \beta}{2W} < {t} \leq \frac{1 + \beta}{2W}}$0, otherwise

To avoid the dc subcarrier, the transmitted signal s_(i)(t) is furthermultiplied with e^(jπaΔf(t−T) ^(CP) ⁾ or e^(−jπaΔf(t−T) ^(CP) ⁾ where ais real-valued number. In an embodiment a=1.

In an embodiment, the signal that is generated for multiple users overdistinct (distributed) frequency resources is transmitted from the sameuser equipment. In this case, the low PAPR properties of the signal doesnot hold any more but the user will be able to transmit at a higher datarate using multiple distributed time-frequency resources.

The modulation data symbols transmitted by a user equipment is usuallyencoded by an error correction code such as block code, convolutionalcode, or a turbo code, followed by a scrambler, interleaver beforemapped to the desired modulation format.

Further, the FDPSF enables the low PAPR waveform design.

The PAPR can be controlled using a suitable choice of constellationrotation factor θ(l), modulation size Q and the FDPSF q(m) given inequation (5). In an embodiment, let

${\theta(l)} = \frac{\pi\left( {l - 1} \right)}{2}$

for real constellations, and for Q-ary complex constellations such asQAM, let

${\theta(l)} = {\frac{\pi\left( {l - 1} \right)}{Q}.}$

For the special case of Q=2, the waveforms may be designed with nearlyconstant envelope by selecting

${{\theta(l)} = \frac{\pi\left( {l - 1} \right)}{2}},$

and by choosing the FDPSF based on the linearized Gaussian pulse that isobtained as the principal pulse in the PAM decomposition of a binary CPMsignal with modulation index 0.5. The time domain samples of the FDPSFqt (n) can be chosen as:

${{{q_{t}(n)} = {p_{0}(t)}}}_{l = {\tau_{0} + \frac{nT}{s}}}$

where p0 (t) is the linearized Gaussian pulse, s is the over-samplingfactor, and the factor BT controls the characteristics of the waveform,and τ₀ is constant time offset, and n is an integer. Since the pulse istime limited, the values of n can be taken in the range

${\frac{{- s}M}{2} \leq n \leq {\frac{sM}{2} - 1}}.$

With an over-sampling rate of s, the Fourier transform of qt (n) isperiodic with a period

$\frac{s}{T}.$

The FDPSF with a span of sMsubcarriers is obtained by taking a sMpointDFT of q_(t)(n) as defined in equation (11). Alternatively, the FDPSFcan be obtained by taking an sM point DFT first as

${\overset{˜}{q}(m)} = {{\sum\limits_{n = 0}^{{sM} - 1}{{q_{t}(n)}e^{\frac{{- {j2}}\mspace{11mu}\pi\; n\; m}{sM}}\mspace{31mu} 0}} \leq m \leq {{sM} - 1}}$

Further, the left and right halves of the DFT output can be swapped sothat the zero frequency components are in the middle. Alternatively, theFDPSG can be obtained using a two sided DFT as

${q(m)} = {{\sum\limits_{n = \frac{- {sM}}{2}}^{\frac{sM}{2} - 1}{{q_{t}(n)}e^{\frac{{- j}\; 2\;\pi\; n\; m}{sM}}\mspace{31mu}\frac{{- s}M}{2}}} \leq m \leq {\frac{sM}{2} - 1}}$

Since the sequence q_(t)(n) is real-valued, in certain cases, it can beappropriately circularly shifted by certain amount before taking the DFTto make the DFT output real. Also, a FDPSF of length less than sM can beapplied by truncating the FDPSF filter at both ends.

Alternative to the proposed designed procedure, one can consider aM₀point DFT of q_(t)(n) where M₀>sM and

${q_{t}(n)} = \left. {p_{0}(t)} \right|_{t = \frac{nT}{s}}$

for

${n = {- \frac{- M_{0}}{2}}},\ldots\mspace{14mu},{\frac{M_{0}}{2} - 1},$

then collect sM points out of M_(o) points by decimating the DFT outputto generate q(m). In yet another alternative implementation, the valuesof q(m)can be obtained by taking samples of p0(f) (that is the Fouriertransform of p0 (t) taken at appropriate intervals).

For the special case of s=1, the technique can design PDPSF withoutexcess BW. In this case, the waveform introduces ISI but has zeromulti-user interference. To obtain the time domain samples for s=1, thetechnique can first generate the samples corresponding to s=2, thenchoose either the even or odd symbol spaced sample sequence to generatethe required FDPSF.

Some examples of values of time domain samples of the q_(t) (n) is givenin the Tables 1 and 2, where the pulse response is forced to be causali.e., the values of qt (n) is positive for n≥0 and takes a zero valuefor n<0. In the Table the values of qt (n) start with n=0. The methoddefines

${\overset{˜}{q}(m)} = {{\sum\limits_{n = 0}^{{sM} - 1}{{q_{t}(n)}e^{\frac{{- j}\; 2\;\pi\; n\; m}{sM}}\mspace{31mu} 0}} \leq m \leq {{sM} - 1}}$

The FDPSF q(m) is obtained after the left and right halves of the DFToutput {tilde over (q)}(m) is swapped so that the zero frequencycomponents are at m=0 . Alternatively, considering the range 0≤n≤sM−1,the causal response qt (n) can be circularly shifted to the left bycertain amount so that the zero^(th) time sample is located at n=⁰ andnegative time samples are located in the left half. In this case, thepulse response is real and symmetric i.e., q_(t)(n)=q_(t)(sM−n). The DFTof this sequence is also real and symmetric i.e., {tilde over(q)}(m)={tilde over (q)}(sM−m). The FDPSF q(m) is obtained after theleft and right halves of the DFT output {tilde over (q)}(m) is swappedso that the zero frequency components in located at m=0 .

TABLE 1 MSK, s = 3 MSK, s = 1 MSK, s = 3 τ₀ = 0 $\tau_{0} = \frac{T}{2}$MSK, s = 2, τ₀ = 0 $\tau_{0} = \frac{T}{2}$ 0.5 0.2588 0.7071 0.70710.866 0.7071 1 0.7071 1 0.9659 0.7071 0 0.866 0.9659 0 0 0.5 0.7071 0 00 0.2588 0 0 0 0 0 0

TABLE 2 BT = 0.3, BT = 0.3, L = 6, s = 1 BT = 0.3, BT = 0.3, L = 6, s =1 L = 6, s = 2 τ₀ = 0 $\tau_{0} = \frac{T}{2}$ L = 6, s = 1 τ₀ = 0$\tau_{0} = \frac{T}{2}$ 0.0007 0.0315 0.0007 0.707 0.0315 0.7057 0.26050.7071 0.2605 0.7057 0.9268 0 0.7057 0.0315 0.2605 0 0.9268 0 0.0007 00.7057 0 0 0 0.2605 0 0 0 0.0315 0 0 0 0.0007 0 0 0

The proposed technique can be used to multiplex data of multiple userswhere each user transmits an approximated continuous phase modulation(CPM) signal. The approximated CPM signal can be obtained byrepresenting CPM a superposition of multiple PAM signals andG-DFT-precoded-OFDM modulation is applied for each PAM component. Onlythe dominant PAM components can be used for transmission. Acorresponding receiver needs to be developed in such cases.

The principal pulse p₀ (t) is the main pulse in Laurent's decomposition[9] is given by

${p_{0}(t)} = \left\{ {{\begin{matrix}{\prod_{k = 1}^{k = L_{1}}{{c\left( {t - {kT}} \right)}\; t\;{\left\lbrack {0,\ {\left( {L_{1} + 1} \right)T}} \right\rbrack}}} & \; \\{{0\mspace{31mu}{otherwise}}\ } & \;\end{matrix}{where}{c(t)}} = \left\{ \begin{matrix}{{\cos\left( {{- \frac{\pi}{2}}{q(t)}} \right)}t\;\left\lbrack {0,{L_{1}T}} \right)} \\{{c\left( {- t} \right)}t\;\left( {{{- L_{1}}T},0} \right\rbrack} \\{{0{t}} \geq {L_{1}T}}\end{matrix} \right.} \right.$

The pulse q(t) is a Gaussian filtered rectangular pulse response definedas

${q(t)} = {\frac{1}{T}\left\lbrack {{Q\left( {\gamma\left( {\frac{t}{T} - \frac{1}{2}} \right)} \right)} - {Q\left( {\gamma\left( {\frac{t}{T} + \frac{1}{2}} \right)} \right)}} \right\rbrack}$

where

${\gamma \cong \frac{2\pi BT}{\sqrt{\left( {\ln(2)} \right)}}},$

BT is a parameter that controls the pulse shape, and

${Q(x)} \cong {\frac{1}{\sqrt{2\pi}}{\int_{x}^{\infty}{e^{- \frac{u^{2}}{2}}d{u.}}}}$

The value of L₁ determines the pulse duration. Typically this value ischosen to be in the range 4-6.

FIG. 2 is a flow diagram illustrating a method 200 for designing awaveform for data communication, according to the embodiments asdisclosed herein. At the step 202, the method involves applying theconstellation specific phase rotation between consecutive data symbolsin the data stream to obtain the constellation rotated data stream. Inan embodiment, the method 200 allows the phase rotation applying unit102 to apply the constellation specific phase rotation betweenconsecutive data symbols in the data stream to obtain the constellationrotated data stream.

At the step 204, the method 200 involves introducing the ISI betweenmodulated data symbols of the constellation rotated data stream. In anembodiment, the method 200 allows the frequency domain pulse shapingfilter 104 to introduce the ISI between modulated data symbols of theconstellation rotated data stream.

The various actions, acts, blocks, steps, and the like in method 200 maybe performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 3a shows the sequence of steps followed in generating a BPSKmodulated G-DFT-precoded-OFDM signal with linearized

Gaussian pulse shaping. At the step 302 a, the method 300 a involvessending/transmitting BPSK modulation data by the transmitter 100. At thestep 304 a, the method 300 a includes performing constellation rotationby pi/2 on the BPSK modulation data using the transmitter 100. At thestep 306 a, the method 300 a includes performing, by the transmitter100, Mi-point DFT after performing constellation rotation. At the step308 a, the method 300 a includes performing, by the transmitter 100, DFTspreading process after performing Mi-point DFT. At the step 310 a, themethod 300 a includes obtaining, by the transmitter 100, the userspecific pulse shaping filter after performing the DFT spreadingprocess. At the step 312 a, the method 300 a includes performing, by thetransmitter 100, an orthogonal/Non-orthogonal subcarrier mapping afterobtaining the user specific pulse shaping filter. At the step 314 a, themethod 300 a includes introducing, by the transmitter 100, a halfsub-carrier shift after performing the orthogonal/Non-orthogonalsubcarrier mapping.

The various actions, acts, blocks, steps, and the like in method 300 amay be performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 3b shows the steps involved for designing the waveform for QAMsystems with arbitrary pulse shaping filter. At the step 302 b, themethod 300 b involves providing PAM or QAM modulation data by thetransmitter 100. At the step 304 b, the method 300 b includes performingconstellation rotation by pi/2 on the modulation data using thetransmitter 100. At the step 306 b, the method 300 b includesperforming, by the transmitter 100, Mi-point DFT after performing theconstellation rotation. At the step 308 b, the method 300 b includesperforming, by the transmitter 100, DFT spreading process afterperforming the Mi-point DFT. At the step 310 b, the method 300 bincludes obtaining, by the transmitter 100, the user specific pulseshaping filter after performing the DFT spreading process. At the step312 b, the method 300 b includes performing, by the transmitter 100, anorthogonal/Non-orthogonal subcarrier mapping after obtaining the userspecific pulse shaping filter. At the step 314 b, the method 300 bincludes introducing, by the transmitter 100, a half sub-carrier shiftafter performing the orthogonal/Non-orthogonal subcarrier mapping.

The various actions, acts, blocks, steps, and the like in method 300 bmay be performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 4a shows the sequence of steps involved in the design of afrequency domain pulse shaping filter using linearized Gaussian pulse.At the step 402 a, the method includes 400 a obtaining, by thetransmitter 100, the linearized Gaussian pulse using Laurent'sdecomposition of GMSK. At the step 404 a, the method includes 400 aoversampling, by the transmitter 100, linearized Gaussian pulse by afactor “S” after obtaining the linearized Gaussian pulse. At the step406 a, the method includes 400 a truncating, by the transmitter 100, thesequence to “sM” points and optionally circularly shifting the sequenceby certain amount. At the step 408 a, the method includes 400 acomputing “sM” point DFT. At the step 410 a, the method includes 400 aswapping, by the transmitter 100, the left and right halves of thesequence with zero frequency in the middle after computing “sM” pointDFT.

The various actions, acts, blocks, steps, and the like in method 400 amay be performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 4b shows the sequence of steps involved in the design of afrequency domain pulse shaping filter for any time domain pulse. At thestep 402 b, the method includes 400 b providing, by the transmitter 100,a time domain pulse shaping function. At the step 404 b, the methodincludes 400 b oversampling, by the transmitter 100, the pulse by afactor “s” after obtaining time domain pulse shaping function. At thestep 406 b, the method includes 400 b truncating, by the transmitter100, the sequence to “sM” points and optionally circularly shifting thesequence by certain amount. At the step 408 b, the method includes 400 bcomputing “sM” point DFT. At the step 410 b, the method includes 400 bswapping, by the transmitter 100, the left and right halves of thesequence with zero frequency in the middle after computing “sM” pointDFT.

The various actions, acts, blocks, steps, and the like in method 400 bmay be performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

In an embodiment, the base station may schedule the users such that theusers located at the cell boundaries or users with low signal-to-noiseratio use the frequency domain pulse shaping filter together withtransmit power boosting. The base station signals to the user at leastone of: the type of frequency domain pulse shaping filter to be used,the number of allocated subcarriers, the location of subcarriers in thetime-frequency plane, the constellation rotation, and the modulationtype. The frequency domain pulse shaping filter may use zero or non-zeroexcess bandwidth. The base station may schedule users such that theusers with low signal-to-noise ratio user narrowband width, frequencydomain pulse shaping with or without excess band width while the usersscheduled in adjacent bands have high signal-to-noise ratio and possiblywider bandwidth allocation. Furthermore, the users may use overlappingset of subcarriers due to excess bandwidth employed at one or moreusers. At the base station receiver, the inter-user-interference causedby the non-orthogonal transmission may not give rise to significantinterference because of the higher received power associated with thehigh signal-to-noise ratio users.

FIG. 5 is a block diagram of various units present in a receiver 500,according to the embodiments as disclosed herein. The receiver 500receives the data stream. The data stream is received in the form ofwaveform designed by the frequency domain pulse shaping filter 104. Thereceiver 500 includes receiving unit 502, a vector/matrix-valued filter504, a converting unit 506, and an eliminating unit 508. A receiverfront end operations such as sampling, synchronization, frequency offsetremoval, I/Q imbalance correction, DC offset correction, clock recovery,and CP (including cyclic prefix and/or suffix) removal and channelestimation operations are similar to a conventional receiver system.Further, the memory introduced by the propagation channel of any givenuser is assumed to be less than that of the CP duration. Furthermore,receiver obtains the overall channel impulse response using pilots andthe knowledge of FDPSF.

The receiving unit 502 is configured to receive the data stream. Afterreceiving the data stream, the vector/matrix-valued filter 504 isconfigured to suppress the ISI between the modulated data symbols in thedata stream. Based on suppressing the ISI between the modulated datasymbols in the data stream, the converting unit 506 is configured toconvert the received data stream to time domain for detection of thesignal.

In an embodiment, the eliminating unit 508 is configured to eliminateconstellation rotation in the received data stream by de-rotating thereceived data stream in the frequency domain.

In an embodiment, the eliminating unit 508 is configured to eliminateconstellation rotation in the received data stream by de-rotating thereceived data stream in the time domain. In an embodiment, theeliminating unit 508 is configured to eliminate the cyclic prefix andthe cyclic suffix from the received data stream after de-rotating thereceived data stream.

The time domain sampled received signal after removing CP is given by

${{y_{t}(n)} = {{{\sum\limits_{i = 1}^{u}{{s_{i,t}(n)} \otimes {h_{i,t}(n)}}} + {{n_{t}(n)}\mspace{31mu} n}} = \frac{- N}{2}}},\ldots\mspace{14mu},{\frac{N}{2} - 1}$

Here s_(i,n)(n) corresponds to the sampled version of the analog signalfor the i^(th) user. The symbol ⊗ denotes linear convolution operation.The noise vector n_(t)(n) is an i.i.d. complex-Gaussian random variableeach with zero-mean and variance

$\frac{\sigma_{n}^{2}}{2}$

per dimension. Note that h_(i,t)(n) is assumed to be a time limitedchannel of the i^(th) user. Taking the N-point two-sided DFT of yt (n),the proposed technique get

$\begin{matrix}{{{\overset{\_}{y}(m)} = {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}{{y_{t}(n)}e^{{- j}2\;\pi\; n\;{m/M}}}}},{m = \frac{- N}{2}},\ldots\mspace{14mu},{\frac{N}{2} - 1}} & 22\end{matrix}$

-   the proposed technique can write y⁻(m) as

$\begin{matrix}{{{\overset{\_}{y}(m)} = {{\sum\limits_{i = 1}^{u}{{q_{i}\left( {m - m_{i}} \right)}{h_{i}(m)}{{\overset{\sim}{x}}_{i}(m)}}} + {n(m)}}},{m = \frac{- N}{2}},\ldots\mspace{14mu},{\frac{N}{2} - 1}} & 23\end{matrix}$

Multi-User System Model:

For the purpose of developing a multi-user generalized MMSE receiver,the proposed techniques assume that a) all the users employ equal numberof subcarriers i.e., Mi=M and b) the proposed techniques apply zeroexcess BW for the users located at the band edges i.e., M ₁=M ₂=M. Theremaining users M _(i)=M for i=2, 3, . . . , L−1. The proposedtechniques have a total of u=L users where L takes a minimum value of 1.For this case

$m_{i} = {{\left( {i - 1} \right)M} - \frac{N - \overset{\_}{M}}{2}}$

for i=2, 3, . . . , L−1 and

${m_{i} = \frac{N - \overset{\_}{M}}{2}},{m_{L} = {{\left( {L - 1} \right)M} - \frac{N - M}{2}}}$

since the proposed method employ zero excess BW at the band edges. As anillustrative example, the proposed techniques restrict to the case whereM≤3M i.e, the frequency domain pulse causes interference to a maximum ofone user located on either side. The receiver 500 can easily generalizedto the case where users apply arbitrary values of M _(i). Furthermore,here the proposed techniques assume that all N subcarriers are utilizedfor data transmission. In practice, the actual number of subcarriers isequal to Nu<N.

In (23), letting

$m = {k + {\left( {i - 1} \right)M} - \frac{N}{2}}$

for k =0,1, . . . , M−1 and i=1,2, . . . , L, let's have

${{y\left( {k + {\left( {i - 1} \right)M}} \right)} = {y\left( {k + {\left( {i - 1} \right)M} - \frac{N}{2}} \right)}},{k = 0},1,\ldots\mspace{14mu},{M - 1},{i = 1},\ldots\mspace{14mu},{L\mspace{14mu}{and}}$${{p_{i}\left( {k + {\left( {i - 1} \right)M}} \right)} = {{q_{i}\left( {k - \frac{{\overset{\_}{M}}_{i}}{2}} \right)}{h_{i}\left( {k + {\left( {i - 1} \right)M} - \frac{N}{2}} \right)}}},{k = 0},1,\ldots\mspace{14mu},{M - 1},{i = 1},\ldots\mspace{14mu},L$

where h_(i)(k) is the frequency domain channel for the i^(th) user and

${{{\overset{˜}{x}}_{i}\left( {k + {\left( {i - 1} \right)M} - \frac{N}{2}} \right)} = {{{x_{i}(k)}\mspace{14mu}{for}\mspace{14mu} i} = 1}},\ldots\mspace{20mu},{L.}$

The proposed detector jointly detects all the L users simultaneouslyusing the generalized MMSE-DFE receiver. The receiver 500 exploits theredundancy (excess BW) contained in the signal. Let us collect multiplecopies of the received signals as

y (k)= H (k)x(k)+ n (k) for k=0, . . . , M−1  24

-   Where

${\overset{\_}{y}(k)} = {{\begin{bmatrix}{y(k)} \\{y\left( {k + M} \right)} \\{y\left( {k + {2M}} \right)} \\{y\left( {k + {3M}} \right)} \\\vdots \\{y\left( {k + {\left( {L - 1} \right)M}} \right)}\end{bmatrix}\mspace{14mu}{\overset{\_}{n}(k)}} = \begin{bmatrix}{n(k)} \\{n\left( {k + M} \right)} \\{n\left( {k + {2M}} \right)} \\{n\left( {k + {3M}} \right)} \\\vdots \\{n\left( {k + {\left( {L - 1} \right)M}} \right)}\end{bmatrix}}$ ${x(k)} = \begin{bmatrix}{x_{1}(k)} \\{x_{2}(k)} \\{x_{3}(k)} \\\vdots \\{x_{L}(k)}\end{bmatrix}$

-   and H(k) is given by

$\mspace{79mu}\begin{bmatrix}{p_{1}(k)} & {p_{2}(k)} & 0 & {0\mspace{14mu}\ldots} & 0 & 0 & 0 & 0 \\0 & {p_{2}\left( {k + M} \right)} & {p_{3}\left( {k + M} \right)} & {0\mspace{14mu}\ldots} & 0 & 0 & 0 & 0 \\0 & {p_{2}\left( {k + {2M}} \right)} & {p_{3}\left( {k + {2M}} \right)} & {p_{4}\left( {k + {2M}} \right)} & \text{?} & 0 & \vdots & \vdots \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\0 & 0 & 0 & 0 & 0 & {\text{?}\left( {k + {\left( {L - 2} \right)M}} \right)} & {\text{?}\left( {k + {\left( {L - 2} \right)M}} \right)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & \text{?} & {\text{?}\left( {k + {\left( {L - 1} \right)M}} \right)}\end{bmatrix}$ ?indicates text missing or illegible when filed

where the proposed techniques illustrate the channel matrix for the casewhere a maximum of two users interfere with any given user. Thisscenario corresponds to the case where the excess BW employed by anyuser is less than 200%.

Multi-user Widely Linear Generalized MMSE Equalizer:

In order to exploit the real-valued nature of modulation symbols, thereceiver first removes the constellation rotation using frequency domainoperations. The first step in the WL receiver is to de-shift thereceived signal by

$\frac{M}{4}$

samples to render the modulation data to be a real-valued signal. Notethat if M is not an integer multiple of 4, constellation de-rotationstep need to be performed in time domain and then transform the signalto frequency domain. After shifting y⁻ (k) by

$\frac{M}{4}$

samples, the proposed techniques get:

ŷ(k)=Ĥ(k)a(k)+{circumflex over (n)}(k)  (25)

Where

${{\overset{\hat{}}{y}(k)} = {y\left( {k \oplus \frac{M}{4}} \right)}},{{\overset{\hat{}}{H}(k)} = {\overset{\_}{H}\left( {k \oplus \frac{M}{4}} \right)}},{{\overset{\hat{}}{n}(k)} = {\overset{\_}{n}\left( {k \oplus \frac{M}{4}} \right)}}$

and the proposed techniques use the fact that

${x_{i}\left( {k \oplus \frac{M}{4}} \right)} = {{a_{i}(k)}.}$

Next, the receiver 500 applies complex conjugation and frequencyreversal operations on ŷ(k)to obtain:

ŷ*(M−k)=Ĥ*(M−k)a(k)+{circumflex over (n)}*(M−k)  (26)

Here a*(M−k)=a(k). Stacking (25) and (26) in column vector format

$\begin{matrix}{\begin{pmatrix}{\overset{\hat{}}{y}(k)} \\{{\overset{\hat{}}{y}}^{*}(k)}\end{pmatrix} = {{\begin{pmatrix} \\{{\hat{H}}^{*}\left( {M - k} \right)}\end{pmatrix}{a(k)}} + \begin{pmatrix}{\hat{n}(k)} \\{{\hat{n}}^{*}\left( {M - k} \right)}\end{pmatrix}}} & (27)\end{matrix}$

In compact matrix form

y(k)=H(k)a(k)+n(k)  (28)

In the proposed WL GMMSE receiver, the received signal is filtered usinga matrix-valued feed-forward filter W(k) to obtain: z(k)=W(k)y(k).Following the approach presented in [13],[14], the proposed techniquesdefine error signal

e(k)={right arrow over (z)}(k)−a(k)  (29)

This is written in time domain as

e _(t)(l)=z _(t)(l)−a _(t)(l)  (30)

Applying orthogonality principle [14]

E(e(k)y†(k))=0, for k=0,1, . . . , M−1  (31)

Substituting (29) in (31) and evaluating the expectation, the FFF can beexpressed as

W(k)=R _(ay)(k)R _(yy) ⁻¹(k)  (32)

Where R_(ay)(k)=E(a(k)y†(k))=R_(aa)(k)H†(k)

-   and R_(yy)(k)=E(y(k)y†(k))=[H(k)R_(aa)(k)H    (k)+R_(nn)(k)]

Here,

-   R_(aa)(k)=E(a(k)a†(k))=Mσ_(a) ²I and-   R_(aa)(k)=E(n(k)n†(k))=Mσ_(n) ²I.    The FFF can be expressed in alternative form as

$\begin{matrix}{{W(k)} = {{R_{aa}(k)}{{H^{\dagger}(k)}\left\lbrack {{{H(k)}{R_{aa}(k)}{H^{\dagger}(k)}} + {R_{nn}(k)}} \right\rbrack}^{- 1}}} & {{~~~~~~~~~~~~~~~~~~~~~}(33)} \\{= {\left\lbrack {{R_{aa}^{- 1}(k)} + {{H^{\dagger}(k)}{R_{nn}^{- 1}(k)}{H(k)}}} \right\rbrack^{- 1}{H^{\dagger}(k)}{R_{nn}^{- 1}(k)}}} & {(34)}\end{matrix}$

Note that (36) follows from applying matrix inversion lemm Let,R_(ee)(k)=E(e(k)e†(k)). Using the optimum FFF, the minimum MSE can beshown to be [13],[14]

$\begin{matrix}{R_{ee} = {{\frac{1}{M^{2}}{\sum\limits_{k = 0}^{M - 1}{R_{ee}(k)}}} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{Q(k)}}}}} & (35)\end{matrix}$

where Q(k)=[R_(aa) ⁻¹(k)+H†(k)R_(nn) ⁻¹H(k)]⁻¹. The symbols ofindividual users are detected using z_(t)(l) using standard slicingmethods.

Conventional GMMSE Receiver

The WL GMMSE receiver design is designed by performing following steps:

-   Step 1: Removal of constellation as a first step is done for the    special case of real constellations only. For complex-valued    constellations, the system works with y(k) directly.-   Step 2: Remarking here that for the special case of s=1, since there    is no multi-user interference among the users, the proposed    conventional or WL GMMSE receiver can be decoupled into multiple    single user conventional or WL MMSE equalizers.

Using Conventional GMMSE receiver, the received signal (25) is filteredusing a matrix-valued feed-forward filter W{circumflex over ( )}(k) toobtain: {circumflex over (z)}(k)=Ŵ(k)ŷ(k). The expressions for the FFFis given by

Ŵ(k)=[R _(aa) ⁻¹(k)+Ĥ†(k)R _({circumflex over (n)}) ⁻¹(k)Ĥ(k)]⁻¹ Ĥ†(k) R_({circumflex over (n)}) ⁻¹(k)  (36)

and the MMSE becomes

$\begin{matrix}{R_{conv} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}\left\lbrack {{R_{aa}^{- 1}(k)} + {{{\overset{\hat{}}{H}}^{\dagger}(k)}{R_{\hat{n}}^{- 1}(k)}{\overset{\hat{}}{H}(k)}}} \right\rbrack^{- 1}}}} & (37)\end{matrix}$

-   The noise covariance term R _(n) (k)=Mσ_(n) ²I.

For complex constellations, the conventional GMMSE receiver can beapplied directly on y⁻ (k) followed by a time domain constellationremoval step after frequency domain equalization.

Conventional single user equalizer:

The multi-user equalizer involves inversion of a channel matrix of sizeL×L. Furthermore, the multi-user user equalizer is applicable only tothe case where M_(i)=M. The following method can be used to detect bothreal and complex constellations. In this case, the equalizer modifiesthe signal model y _(i)(k) where the elements of y _(i)(k)

¹(A+BCD)⁻¹ =A ⁻ +A ⁻¹ BC ⁻¹ +DA ⁻¹ B ⁻¹ DA ⁻¹

are formed by appropriately collecting the subcarriers of interest.Assuming Mi be the allocated for the user, the received signal model y_(i)(k) can be modified as

${\overset{\_}{y}(k)} = \begin{bmatrix}\vdots \\{y\left( {k + {\left( {i - 2} \right)M_{i}}} \right)} \\{y\left( {k + {\left( {i - 1} \right)M_{i}}} \right)} \\{y\left( {k + \left( {iM_{i}} \right)} \right)} \\\vdots\end{bmatrix}$ ${{\overset{\_}{h}}_{i}(k)} = {{\begin{bmatrix}\vdots \\{p_{i}\left( {k + {\left( {i - 2} \right)M_{i}}} \right)} \\{p_{i}\left( {k + {\left( {i - 1} \right)M_{i}}} \right)} \\{p_{i}\left( {k + \left( {iM_{i}} \right)} \right)} \\\vdots\end{bmatrix}\mspace{31mu}{{\overset{\_}{n}}_{i}(k)}} = \begin{bmatrix}\vdots \\{n_{i}\left( {k + {\left( {i - 2} \right)M_{i}}} \right)} \\{n_{i}\left( {k + {\left( {i - 1} \right)M_{i}}} \right)} \\{n_{i}\left( {k + {(i)M_{i}}} \right)} \\\vdots\end{bmatrix}}$

can be used to develop the single user equalizer. Using this, for thecase of conventional signal model, the proposed techniques can rewrite y_(i)(k) as

$\begin{matrix}{{{{\overset{\_}{y}}_{i}(k)} = {{{{\overset{\_}{h}}_{i}(k)}{a_{i}(k)}} + {\sum\limits_{i \neq j}{{{\overset{\_}{h}}_{j}(k)}{a_{j}(k)}}} + {\overset{\_}{n}(k)}}},\mspace{14mu}{i = 1},2,\ldots\mspace{14mu},L} & (38)\end{matrix}$

where h_(i)(k) is the i^(th) column of H(k) with certain rows containingzeros in h⁻ i(k) are eliminated. The received signal (38) is filteredusing a vector valued feed-forward filter w _(i)(k) to obtain:z(k)=W(k)y _(i)(k) where z _(i)(k) is a scalar-valued frequency domainequalized signal for the i^(th) user. Following the MMSE approach, theexpression for FFF is given by:

w _(i)(k)=[σ_(a) _(i) ² +h _(i) †R _(i,n) ⁻¹(k) h _(i)(k)]⁻¹ h _(i)†(k)R _(i,n) ⁻¹(n)  (39)

Where,

$\begin{matrix}{{R_{i,\overset{\_}{n}}(k)} = {{\sum\limits_{i \neq j}{{{\overset{\_}{h}}_{j}(k)}{{\overset{\_}{h}}_{j}^{\dagger}(k)}\sigma_{a_{j}}^{2}}} + \sigma_{n}^{2}}} & (40)\end{matrix}$

where σ_(ai) ² is the variance of the i^(th) user data. The MSE for thei^(th) user is given by

$\begin{matrix}{{\overset{\hat{}}{r}}_{i,{ee}} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}\left\lbrack {\sigma_{a_{i}}^{2} + {{{\overset{\_}{h}}_{j}^{\dagger}(k)}{R_{i,\hat{n}}^{- 1}(k)}{{\overset{\_}{h}}_{i}(k)}}} \right\rbrack^{- 1}}}} & (41)\end{matrix}$

Taking the IDFT of z _(i)(k) gives the time domain decision variable fordetecting i^(th) user. The constellation de-rotation can be performed onz _(i)(k).

Single user WL equalizer:

The single user WL equalizer is designed by collecting the signal (38)and its complex-conjugate and reversed copy in a column format.

$\begin{pmatrix}{\overset{\_}{y}(k)} \\{{\overset{\_}{y}}^{*}\left( {M_{i} - k} \right)}\end{pmatrix} = {{\begin{pmatrix}{{\overset{\_}{h}}_{i}(k)} \\{{\overset{\_}{h}}_{i}^{*}\left( {M_{i} - k} \right)}\end{pmatrix}\ {a_{i}(k)}} + {\sum\limits_{j \neq i}{\begin{pmatrix}{{\overset{\_}{h}}_{j}(k)} \\{{\overset{\_}{h}}_{j}^{*}\left( {M_{i} - k} \right)}\end{pmatrix}{a_{j}(k)}}} + \begin{pmatrix}{\overset{\_}{n}(k)} \\{{\overset{\_}{n}}^{*}\left( {M_{i} - k} \right)}\end{pmatrix}}$

In compact matrix form:

$\begin{matrix}{{\overset{\sim}{y}(k)} = {{{{\overset{\sim}{h}}_{i}(k)}{a_{i}(k)}} + {\sum\limits_{i \neq j}{{{\overset{\sim}{h}}_{j}(k)}{a_{j}(k)}}} + {\overset{\sim}{n}(k)}}} & (43)\end{matrix}$

The received signal (43) is filtered using vector-valued feed-forwardfilter {tilde over (w)}_(i)(k) to obtain {tilde over (z)}_(i)(k)={tildeover (w)}_(i)(k){tilde over (y)}_(i)(k): where z_(i)(k) is a scalarvalued frequency domain equalized signal for the i^(th) user. Followingthe MMSE approach, the expression for FFF is given by:

{tilde over (w)} _(i)(k)=[σ_(a) _(i) ² +{tilde over (h)} _(i)†(k)R_(i,ñ) ⁻¹(k)h _(i)]^(−i) {tilde over (h)} _(i)†(k) R _(i,ñ) ⁻¹(k)  (44)

where,

$\begin{matrix}{{R_{i,\overset{\sim}{n}}(k)} = {{\sum\limits_{i \neq j}{{{\overset{\sim}{h}}_{j}(k)}{{\overset{\sim}{h}}_{j}^{\dagger}(k)}\sigma_{a_{j}}^{2}}} + \sigma_{n}^{2}}} & (45)\end{matrix}$

where σ_(ai) ² is the variance of the i^(th) user data. The MSE for thei^(th) user is given by

$\begin{matrix}{{\overset{\sim}{r}}_{i,{ee}} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}\left\lbrack {\sigma_{a_{i}}^{2} + {{{\overset{\sim}{h}}_{j}^{\dagger}(k)}{R_{i,\overset{\sim}{n}}^{- 1}(k)}{{\overset{\sim}{h}}_{i}(k)}}} \right\rbrack^{- 1}}}} & (46)\end{matrix}$

Taking the IDFT of z _(i)(k) gives the time domain decision variable fordetecting ith user. The constellation de-rotation can be performed on{tilde over (z)}_(i)(k).

FIG. 6 a flow diagram illustrating a method 600 for processing thereceived data stream, according to the embodiments as disclosed herein.At the step 602, the method 600 includes receiving the data stream. Inan embodiment, the method 600 allows the receiving unit 502 to receivethe data stream. In an embodiment, the data stream comprises the ISIbetween modulated data symbols of the data stream.

At the step 604, the method 600 includes suppressing the ISI between themodulated data symbols in the data stream. In an embodiment, the method600 allows the vector/matrix-valued filter 504 to suppress the ISIbetween the modulated data symbols in the data stream.

At the step 606, the method 600 includes converting the received datastream to time domain for detection of a signal. In an embodiment, themethod 600 allows the converting unit 506 to convert the received datastream to the time domain for detection of the signal after suppressingthe ISI.

At the step 608, the method 600 includes eliminating the constellationrotation in the received data stream. At the step 610, the method 600includes eliminating the cyclic prefix or cyclic suffix from thereceived data stream.

The various actions, acts, blocks, steps, and the like in method 600 maybe performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 7 shows the sequence of steps involved during signal reception inthe GMMSE receiver design. At the step 702, the method 700 includesproviding a vector-matrix representation of multi-user signals in thefrequency domain using the M-subcarrier for each user. At the step 704,the method 700 includes performing frequency domain filtering of signalsusing the multi-user GMMSE receiver after providing the vector-matrixrepresentation of multi-user signals in the frequency domain. At thestep 706, the method 700 includes converting, by the receiver, each userdata to time domain for signal detection after performing frequencydomain filtering of signals.

The various actions, acts, blocks, steps, and the like in method 700 maybe performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 8 shows the sequence of steps involved in during signal receptionthe single user MMSE receiver design. At the step 802, the method 800includes providing the vector-matrix representation of the single-usersignals with the interference in the frequency domain using theM-subcarrier for each user. At the step 804, the method 800 includesperforming the frequency MMSE filtering of signals using the single userMMSE receiver after providing the vector-matrix representation of thesingle-user signals with the interference in the frequency domain. Atthe step 806, the method 800 includes converting each user data to timedomain for the signal detection after performing the frequency MMSEfiltering of signals.

The various actions, acts, blocks, steps, and the like in method 800 maybe performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

FIG. 9 shows the sequence of steps during signal reception in the singleuser WL MMSE receiver design. At the step 902, the method 900 includesproviding the vector-matrix representation of single-user signal withinterference in the frequency domain using the M-subcarrier for eachuser. At the step 904, the method 900 includes performing constellationde-rotation frequency/time domain after providing the vector-matrixrepresentation of single-user signal with interference in the frequencydomain. At the step 906, the method 900 includes performing frequency WLMMSE filtering of signals and it's conjugated and frequency reversedcopy using single user WL MMSE receiver. At the step 908, the method 900includes converting each user data to the time domain for the signaldetection.

The various actions, acts, blocks, steps, and the like in method 900 maybe performed in the order presented, in a different order orsimultaneously. Further, in some embodiments, some actions, acts,blocks, steps, and the like may be omitted, added, modified, skipped,and the like without departing from the scope of the invention.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the embodiments herein that others can, byapplying current knowledge, readily modify and/or adapt for variousapplications such specific embodiments without departing from thegeneric concept, and, therefore, such adaptations and modificationsshould and are intended to be comprehended within the meaning and rangeof equivalents of the disclosed embodiments. It is to be understood thatthe phraseology or terminology employed herein is for the purpose ofdescription and not of limitation. Therefore, while the embodimentsherein have been described in terms of preferred embodiments, thoseskilled in the art will recognize that the embodiments herein can bepracticed with modification within the spirit and scope of theembodiments as described herein.

What is claimed is: 1-24. (canceled)
 25. A method for generating awaveform by one or more transmitters with a plurality of orthogonalfrequency division multiplexing (OFDM) symbols in a communicationnetwork, the method comprising: generating, by the one or moretransmitters, a Discrete Fourier transform (DFT)-precoded-OFDM symbol,wherein the DFT-precoded-OFDM symbol generation comprises: a phaserotation between successive modulated data elements of a transmitterspecific modulated data sequence, a DFT operation, a transmitterdependent subcarrier mapping, a spectrum shaping filtering, an inverseFourier transform operation, and adding at least one of a cyclic prefixand a cyclic suffix, wherein said transmitter dependent subcarriermapping comprises localized sub-carriers and/or distributedsub-carriers, and wherein said transmitter dependent subcarrier mappingis one of mutually fully overlapping, mutually partially overlapping andmutually non-overlapping.
 26. The method as claimed in claim 25, whereinthe modulated data sequence is one of BPSK, QPSK and M-ary QAM.
 27. Themethod as claimed in claim 26, wherein the phase rotation is 90 degreesfor the BPSK modulated data sequence.
 28. The method as claimed in claim26, wherein the phase rotation is 180/M degrees for the M-ary QAMmodulated data sequence, said M is size of the M-ary QAM.
 29. The methodas claimed in claim 25, wherein the DFT operation is one of a one-sidedDFT and a two-sided DFT.
 30. The method as claimed in claim 25, whereinthe spectrum shaping filtering comprises coefficients that are afunction of samples of a linearized Gaussian pulse.
 31. The method asclaimed in claims 30, wherein the function comprises one of a one-sidedDFT and a two-sided DFT.
 32. The method as claimed in claim 25, whereinthe spectrum shaping filtering comprises coefficients that are afunction of one of the three sequences [1], [0.707 0.707] and [0.26050.9268 0.2605].
 33. The method as claimed in claim 32, wherein thefunction comprises one of a one-sided DFT and a two-sided DFT.
 34. Themethod as claimed in claim 25, wherein the one or more transmitters areassociated with one or more users.
 35. The method as claimed in claim25, wherein the one or more transmitters are associated with one or moreantennas of a user.
 36. The method as claimed in claim 25, wherein theone or more transmitters are associated with one or more users and oneor more antennas of the users.
 37. The method as claimed in claim 25,wherein the spectrum shaping filtering is associated with one of a user,a transmitter and antennas of a user.
 38. A method of receiving a signalwhich includes pilots and data, wherein said method comprises:estimating a channel impulse response using at least one of the pilotsand coefficients of a spectrum shaping filter; and equalizing a portionof the received signal according to the estimated channel impulseresponse.
 39. The method as claimed in claim 38, wherein the equalizingis one of a minimum mean square error (MMSE) and a Widely linear(WL)-MMSE.
 40. The method as claimed in claim 38, wherein the receivedsignal is collected from one or more antennas, and wherein theequalizing is operable to obtain data of one or more users.